You've seen the pictures and now you want to give it a go .
The best camera for your early steps onto the streets is probably the one you already have, it may be your camera phone or the one you take on holiday. ( I rate the old Olympus Trip film camera as a great street camera.)
The most important thing is the mind set you bring to your new photographic efforts. You should ask yourself what you are trying to achieve from your early SP efforts, looking at the work of other street togs will help you understand the medium and give you a few ideas.
The first thing you will realize is that its not as easy as it first appears, organizing the chaos of life into meaningful frame sized chunks is demanding and your "failure" rate will be high in the early days, to be honest the failure rate will always be high, that is the nature of SP.
Remember that SP is art photography don't get bogged down with the technical stuff, find a scenario that might develop into a picture opportunity and be patient, wait and watch and then watch some more, the right moment will present itself and you will be ready to capitalise on the moment, a gunslingers reactions are not necessary if you have visualised how a scene might develop correctly.
In short become a people watcher, notice what is happening and try to predict what might happen next and be prepared to capture it. Don't let the photographic technicalities get between you and the moment, keep it simple move slowly and blend into the scene.
This is a personal journey, learn from your failures and understand why the good pix are good and think about how you can make them better. Treat your subjects (strangers) with respect and a smile, do not photograph children during your early days as society does not embrace nervous looking adults pointing lenses towards kids. The paranoia of society is on the rise and you should realize that street photographers are viewed by some as either terrorists or pedophiles.
Street Photography is a lawful activity in public places and is protected by article 10 of the European Convention. This does not give you license to run amok, remember the idea is to blend in and create candid real images.
Street Photography should be thought of as "JAZZ" rather than classical and the creative freedom of street should be enjoyed and exploited.
Good luck with your early efforts and welcome to the street photography community.